Symmetry breaking, off-diagonal scattering, and Josephson currents in mesoscopic weak links

Abstract

In a unified description of superconductor–normal-metal–superconductor (SNS) and superconductor-semiconductor-superconductor (SSmS) junctions with mean free paths exceeding the N- or Sm-layer thickness it is shown how off-diagonal (Andreev) scattering from spatial variations of the pair potential in competition with diagonal scattering from interface potentials, mismatches of Fermi energies, and effective masses determines the quasiparticle states and Josephson current densities. The bound states with subgap energies provide the main channels for Cooper pair transfer via Andreev scattering. Scattering states only contribute to the net Cooper pair transfer in narrow ‘‘resonance’’ windows just above the gap at energies which are a continuation of the bound-states spectrum. The corresponding part of the Josephson current density flows in or against the direction of the bias current, depending upon the phase difference and thickness of the nonsuperconducting layer. The current contributions from the bound and scattering states oscillate opposite to each other as functions of this thickness. The weakening of phase coherence by increases of temperature and interface potentials and the corresponding approach to the sinusoidal current-phase relationship are discussed. Perturbation theory and comparison with the exact calculations show that the Bardeen-Johnson current density is exact in the limit of thin-film SNS junctions and a good approximation in junctions with cross-sectional dimensions of the S-banks much larger than the London penetration depth, if the N-layer thickness 2a exceeds considerably the BCS coherence length ξ0. The possibility of Josephson-Bloch oscillations in SSmS junctions is discussed.

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